论文标题

托马斯$ - $ whitehead重力的一般结构

General structure of Thomas$-$Whitehead gravity

论文作者

Brensinger, Samuel, Heitritter, Kenneth, Rodgers, Vincent, Stiffler, Kory

论文摘要

Thomas-Whitehead(TW)重力是在D维歧管上进行投影的重力模型,该模型通过重新聚体不变性与弦理论密切相关。未参数化的大地学是将弦理论和更高维度重点联系在一起的无处不在的结构。这是通过特雷西·托马斯(Tracy Thomas)的投射几何形状实现的。由于托马斯(Thomas)和后来的怀特海(Whitehead),投影连接承认了一个组件,即一对一与Virasoro代数的共同连接元素一对一。该组件在文献中称为diffemormormormist字段$ \ MATHCAL {d} _ {ab} $。还表明,在四个维度上,当$ \ nathcal {d} _ {ab} $与爱因斯坦公制成正比时,两种动作以宇宙学常数折叠到爱因斯坦 - 希尔伯特的动作。这些先前的结果仅限于特定指标,例如Polyakov 2d \公制,或仅限于保留体积的坐标。在本文中,我们回顾了两次重力,并得出了明显不变和一般坐标不变的量规不变的TW动作。我们得出了TW动作的协变场方程,并展示了Fermionic Fields如何将其与规格不变理论相对。独立字段是度量张量$ g_ {ab} $,基本的投影不变$π^{a} _ {\,\,\,\,bc} $和diffeomorphism field $ \ MATHCAL $ \ MATHCAL d_ {ab {ab {ab} $。

Thomas-Whitehead (TW) gravity is a projectively invariant model of gravity over a d-dimensional manifold that is intimately related to string theory through reparameterization invariance. Unparameterized geodesics are the ubiquitous structure that ties together string theory and higher dimensional gravitation. This is realized through the projective geometry of Tracy Thomas. The projective connection, due to Thomas and later Whitehead, admits a component that in one dimension is in one-to-one correspondence with the coadjoint elements of the Virasoro algebra. This component is called the diffeomorphism field $\mathcal{D}_{ab }$ in the literature. It also has been shown that in four dimensions, the TW\ action collapses to the Einstein-Hilbert action with cosmological constant when $\mathcal{D}_{ab}$ is proportional to the Einstein metric. These previous results have been restricted to either particular metrics, such as the Polyakov 2D\ metric, or were restricted to coordinates that were volume preserving. In this paper, we review TW gravity and derive the gauge invariant TW action that is explicitly projectively invariant and general coordinate invariant. We derive the covariant field equations for the TW action and show how fermionic fields couple to the gauge invariant theory. The independent fields are the metric tensor $g_{ab}$, the fundamental projective invariant $Π^{a}_{\,\,\,bc}$, and the diffeomorphism field $\mathcal D_{ab}$.

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